Option Question about Delta

Let's push things a bit further: assuming risk neutral probabilities and if one wishes a "risk neutral probability of exercise", what is the worse case of the erroe in a delta vs. the prob approximation?

The usefulness of debating this issue is not to reach a false/true type of answers, but rather to further one's understanding by putting things through a "microscope", because from afar all things may look similar, but from a closer view might be able to see pimples in a knowledge face.

Magnifying mirrors have value.
 
Quote from sle:

Ok, you've convinced us that you are a big swinging dick and that I am actually a teenager posting on ET from my moms house.

However, the points I am trying to make for a noob (and I will reiterate them for you):

(1) Delta of a vanilla option is a reasonable approximation of probability being ITM at expiry, as long as volatility/carry are low enough and option expiry short enough (e.g. 3m S&P 500 options in a normal environment).

(2) Assuming the limitations above, for most trading applications of "probability" (for example, calculating relative value of the longer-dated skew via probability-adjusted dvega/dspot), delta and gammaP are sufficient.

Do you agree or do you not agree? Also, do you really believe that I do not understand the impact of volatility and carry on the delta-neutral strike, given that in the very first post I said "carry/ito adjusted probability"?
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SLE, the CFA Curriculum's definition of delta is how much the option will move for a $1 move in the underlying.

<b>It has nothing to do with those probabilities.</b>

A quicker example we could try is the Q's strike 57 options. Somebody can go get a delta calculator, put in the prices, add something for the risk free rate, and we'll have our delta.

Then, to further the experiment, we can see if the options price action from a $1 move in QQQ actually came out to approximately be delta.

There is no reason to test the probability logic when it has nothing to do with that.

Someone get me the 57 strike delta, then we can wait until there's a $1 move in the Q's.

BRB.
 
Quote from bwolinsky:

SLE, the CFA Curriculum's definition of delta is how much the option will move for a $1 move in the underlying.

<b>It has nothing to do with those probabilities.</b>
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Two variables can be different in terms of their definition, but this does not mean that the values they would assume cannot be equal.
 
Quote from tradingjournals:

Could you redo your anal ysis for ATM strike, distinguishing what moves from what does not move?
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Your missing the point. It's probability. It's not absolute. The same way delta is only accurate if vol does not change. It's just an estimate. If you've ever bought a 50 delta call and the stock goes up a dollar, and the call only increases by .40, you'll understand.

Greeks are used for risk and for hedging. They're estimates based on a mathematical model that's only as good as the assumptions, many of which change all the time. You can't use delta to determine where a stock is going to trade in the future. I never said that. But the delta represents a hedge ratio and a probability with in the model, of the chance of an occurrence. The same way insurance on your car is priced based on the probability of you get into an accident or having your car stolen. It does not mean it will ever happen to you. A 25 delta on a put in AAPL does not mean that 25% of the time it will happen. It's only saying there is a 25% chance built into the pricing.
 
Quote from Martinghoul:

Now that we have our true resident options experts, bwol and tj, weighing in on the subject, it's officially hopeless.
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Is your screen name Matinghoul or Martingfoul?
 
Quote from rmorse:

Your missing the point. It's probability. It's not absolute. The same way delta is only accurate if vol does not change. It's just an estimate. If you've ever bought a 50 delta call and the stock goes up a dollar, and the call only increases by .40, you'll understand.
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Are sure that it is not you who is missing the point? Give us the numbers for deltas ATM, and the prob. of exercise ATM. I bet you know how to run a BS calculator, and you should then be able to give us those numbers in a flash.
 
Quote from rmorse:

If you've ever bought a 50 delta call
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While you are thinking/running numbers, could you also care to find an example where an ATM(fwd) (alive) call has a delta of 50?
 
Quote from bwolinsky:

SLE, the CFA Curriculum's definition of delta is how much the option will move for a $1 move in the underlying.

<b>It has nothing to do with those probabilities.</b>

A quicker example we could try is the Q's strike 57 . Somebody can go get a delta calculator, put in the prices, add something for the risk free rate, and we'll have our delta.

Then, to further the experiment, we can see if the options price action from a $1 move in QQQ actually came out to approximately be delta.

There is no reason to test the probability logic when it has nothing to do with that.

Someone get me the 57 strike delta, then we can wait until there's a $1 move in the Q's.

BRB.
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Using an option pricing calculator Black-Scholes options pricing model with the following settings:

Current Security Price 57.81
Excercise Price 57
January 13th options
Interest Rate 1
Security Volatility 15
Dividend Rate 0.165
Call Price $1 Implied Vol 0.22
Put Price $0.46 Implied Vol 0.28

Fair Value of the call is 0.8353 and fair value of the put is .1481, both overvalued.

The Delta Call Ratio is 0.7537 and the Delta Put Ratio is -0.2441.

We know these values from Fidelity and the close Friday, so we'll just have to wait for a $1 move in QQQ to see if indeed the call option did change $0.7537 and the Delta Put ratio did change inversely $0.2441.

There is no such thing as a delta of 50, but he probably meant 0.5.
 
Quote from rmorse:

Your missing the point. It's probability. It's not absolute. The same way delta is only accurate if vol does not change. It's just an estimate. If you've ever bought a 50 delta call and the stock goes up a dollar, and the call only increases by .40, you'll understand.

Greeks are used for risk and for hedging. They're estimates based on a mathematical model that's only as good as the assumptions, many of which change all the time. You can't use delta to determine where a stock is going to trade in the future. I never said that. But the delta represents a hedge ratio and a probability with in the model, of the chance of an occurrence. The same way insurance on your car is priced based on the probability of you get into an accident or having your car stolen. It does not mean it will ever happen to you. A 25 delta on a put in AAPL does not mean that 25% of the time it will happen. It's only saying there is a 25% chance built into the pricing.
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No Robert, It would be a 25% chance if the underlying followed a brownian motion and it had a drift that equals cost of carry. And it's wrong in real life. Cmon.

The second point is that it's model dependent when used for option pricing.
 
Quote from bwolinsky:

Using an option pricing calculator Black-Scholes options pricing model with the following settings:

Current Security Price 57.81
Excercise Price 57
January 13th options
Interest Rate 1
Security Volatility 15
Dividend Rate 0.165
Call Price $1 Implied Vol 0.22
Put Price $0.46 Implied Vol 0.28

Fair Value of the call is 0.8353 and fair value of the put is .1481, both overvalued.

The Delta Call Ratio is 0.7537 and the Delta Put Ratio is -0.2441.

We know these values from Fidelity and the close Friday, so we'll just have to wait for a $1 move in QQQ to see if indeed the call option did change $0.7537 and the Delta Put ratio did change inversely $0.2441.

There is no such thing as a delta of 50, but he probably meant 0.5.
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If you guys want to test it before the move becomes a full dollar divide the move in the Q's by $1 and multiply the delta ratio.

In the past whenever I tried to validate this method myself, I follow a $0.10 move in the Q's is also 10% of $1, so the option every 0.1 will change by 0.7537*0.1 and 0.2441*0.1, and the same for a $0.5 move, 0.7537*0.5 and 0.2441*0.5, etc.

Since we may not get a $1 move in the Q's before friday, we can validate the right use of Delta very quickly once options open up.
 
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